Topological phase transition in the nu =2/3 quantum Hall effect

Rigorous analysis of the topologically protected edge states in the quantum spin Hall phase of the armchair ribbon geometry

Studying the edge states of a topological system and extracting their topological properties is of great importance in understanding and characterizing these systems. In this paper, we present a novel analytical approach for obtaining explicit expressions for the edge states in the Kane-Mele model within a ribbon geometry featuring armchair boundaries. Our approach involves a mapping procedure that transforms the system into an extended Su-Schrieffer-Heeger model, specifically a two-leg ladder, in momentum space. Through rigorous derivation, we determine various analytical properties of the edge states, including their wave functions and energy dispersion. Additionally, we investigate the condition for topological transition by solely analyzing the edge states, and we elucidate the underlying reasons for the violation of the bulk-edge correspondence in relatively narrow ribbons. Our findings shed light on the unique characteristics of the edge states in the quantum spin Hall phase of the Kane-Mele model and provide valuable insights into the topological properties of such systems.

Light-Induced Fractional Quantum Hall Phases in Graphene

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at nonzero relative angular momentum can become dominant, resembling a hollow-core pseudopotential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν=1/2 and ν=2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids

We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. We find that the transition is signaled by a sharp increase in the sensitivity of a suitably averaged entanglement entropy with respect to disorder-the magnitude of its disorder derivative appears to diverge in the thermodynamic limit. We also study the level statistics of the entanglement spectrum as a function of disorder. However, unlike the dramatic phase-transition signal in the entanglement entropy derivative, we find a gradual reduction of level repulsion only deep in the Anderson insulating phase.

Fractional topological phases and broken time-reversal symmetry in strained graphene

We show that strained or deformed honeycomb lattices are promising platforms to realize fractional topological quantum states in the absence of any magnetic field. The strain-induced pseudomagnetic fields are oppositely oriented in the two valleys and can be as large as 60-300 T as reported in recent experiments. For strained graphene at neutrality, a spin- or a valley-polarized state is predicted depending on the value of the on-site Coulomb interaction. At fractional filling, the unscreened Coulomb interaction leads to a valley-polarized fractional quantum Hall liquid which spontaneously breaks time-reversal symmetry. Motivated by artificial graphene systems, we consider tuning the short-range part of interactions and demonstrate that exotic valley symmetric states, including a valley fractional topological insulator and a spin triplet superconductor, can be stabilized by such interaction engineering.